Q: A mixture contains 40% n-pentane and 60% n-hexane by mole. If the vapor pressures of pure n-pentane and n-hexane at 100°C are $$P^o_{pentane} = 4.0$$ atm and $$P^o_{hexane} = 1.5$$ atm, what is the total vapor pressure above the liquid according to Raoult's Law?

$$P = (0.4 \times 4.0) + (0.6 \times 1.5) = 2.6$$ atm

Q: A gas mixture at 755 mmHg contains 9.48 mol% water in the gas phase. At what temperature will water begin to condense? (Assume $$P^o_{H_2O} at $$that temperature equals the partial pressure of water in the mixture.)

When $$P^o_{H_2O} = 0.0948 \times 755$$ mmHg

Question 1

Which of the following best describes vapor pressure ($$P^o) in $$the context of vapor-liquid equilibrium?

Accepted Answer

The pressure exerted by the vapor when the liquid and vapor of a pure component are in equilibrium.

Question 2

According to Raoult's Law, what is the partial pressure of component $$i in $$the vapor phase at equilibrium?

Accepted Answer

$$P_i = x_i P^o_i$$

Question 3

A mixture contains 40% n-pentane and 60% n-hexane by mole. If the vapor pressures of pure n-pentane and n-hexane at 100°C are $$P^o_{pentane} = 4.0$$ atm and $$P^o_{hexane} = 1.5$$ atm, what is the total vapor pressure above the liquid according to Raoult's Law?

Accepted Answer

$$P = (0.4 	imes 4.0) + (0.6 	imes 1.5) = 2.6$$ atm

Question 4

Which equation is used to estimate the vapor pressure of a substance over a limited temperature range using tabulated constants?

Accepted Answer

$$\log_{10} P^* = \frac{A - B/(T + C)}{T}$$

Question 5

In a multi-component system, which law states that the total pressure is the sum of the partial pressures of each component?

Accepted Answer

Dalton's Law of Partial Pressures: $$P = P_A + P_B + \cdots + P_N$$

Question 6

A gas mixture at 755 mmHg contains 9.48 mol% water in the gas phase. At what temperature will water begin to condense? (Assume $$P^o_{H_2O} at $$that temperature equals the partial pressure of water in the mixture.)

Accepted Answer

When $$P^o_{H_2O} = 0.0948 	imes 755$$ mmHg

Question 7

If a liquid solution contains equimolar amounts of n-pentane, cyclopentane, and benzene at 60°C, how do you calculate the total pressure of the gaseous phase in equilibrium?

Accepted Answer

Sum the partial pressures: $$P_{total} = x_{pentane} P^o_{pentane} + x_{cyclopentane} P^o_{cyclopentane} + x_{benzene} P^o_{benzene}$$

Question 8

Which of the following statements about equilibrium in vapor-liquid systems is correct?

Accepted Answer

At equilibrium, the rate of vaporization equals the rate of condensation.

Question 9

Given the DIPPR equation for vapor pressure: $$\ln P^o = A + \frac{B}{T} + C \ln T + D T^E$$, which variable represents the temperature?

Accepted Answer

$$T$$

Question 10

A closed container holds a mixture of n-pentane and n-hexane at 100°C and 3.5 atm. If the vapor phase is found to be richer in n-pentane than the liquid phase, what does this indicate about the relative volatility of n-pentane compared to n-hexane?

Accepted Answer

n-pentane is more volatile than n-hexane.

Question 11

In a vapor-liquid equilibrium calculation, which step is necessary to determine the mass % composition of the vapor mixture in equilibrium?

Accepted Answer

Calculate the mole fraction of each component in the vapor phase, then convert to mass using molecular weights.

Question 12

Which of the following is a correct application of Raoult's Law for a binary mixture?

Accepted Answer

$$P = x_A P^o_A + x_B P^o_B$$

Question 13

A liquid mixture is heated until it reaches equilibrium with its vapor. Which factor will NOT affect the vapor pressure of the mixture?

Accepted Answer

The color of the liquid.

Question 14

If the total pressure above a liquid mixture is less than the sum of the pure component vapor pressures, what does this suggest about the mixture?

Accepted Answer

The mixture exhibits negative deviation from Raoult's Law.

Question 15

Which of the following is the correct expression for the mole fraction of component A in the vapor phase for an ideal gas mixture?

Accepted Answer

$$y_A = \frac{P_A}{P}$$

Question 16

A mixture of n-pentane, cyclopentane, and benzene is saturated with vapor at 60°C. If the vapor pressures of the pure components are known, what is the first step in calculating the equilibrium vapor composition?

Accepted Answer

Calculate the partial pressure of each component using Raoult's Law.

Question 17

Which real-world scenario best illustrates the concept of vapor-liquid equilibrium?

Accepted Answer

Water droplets forming on the outside of a cold bottle due to condensation.

Question 18

If the boiling point of water is to be determined at a pressure of 125 kPa, which equation should be used to find the temperature?

Accepted Answer

Use the DIPPR equation for water vapor pressure and solve for $$T$$ when $$P^o = 125$$ kPa.

Vapor-Liquid Equilibrium: Principles, Laws, and Calculations

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